Q: A collection of 8 point charges, each with charge $$q = 100\ \mathrm{nC}$$, are arranged on the corners of a cube of side length $$10\ \mathrm{cm}. If $$the electric potential is defined to be zero at infinity, what is the potential at the center of the cube?

$$6.6 \times 10^4$\ \mathrm{Volts}$$

Q: Four point charges, each with charge $$q = 50\ \mathrm{nC}$$, are arranged in a square with side length $$10\ \mathrm{cm}. If a $$proton is at the center of the square and is given an initial velocity of $$10^5$$\ \mathrm{m/s}$$ in the $$+\hat{y}$$ direction, what is its velocity when it is very far away from the square? (Neglect energy loss, and use m_p = 1.67$$ \times $$10^{-27}$$\ \mathrm{kg}$$, q_p = 1.6$$ \times $$10^{-19}$$\ \mathrm{C}$$)

$$1.4 \times 10^5$\ \mathrm{m/s}$$

Q: Three point charges, each with charge $$q = 72\ \mathrm{nC}$$, are arranged in an equilateral triangle with side length $$1\ \mathrm{m}. $$What is the magnitude of the electrostatic force on one of the charges from the combined electric field of the other two?

$$6.1 \times 10$$^{-3}$$\ \mathrm{N}$$

Q: A parallel-plate capacitor has a plate separation of $$1\ \mathrm{mm}$$ and a potential difference of $$5.1\ \mathrm{V}$$ across the plates. What is the magnitude of the electric field between the plates?

$$5.1 \times 10^3$\ \mathrm{N/C}$$

Q: Suppose there is a semi-infinite line charge along the positive $$x-$$axis with charge density $$\lambda = 2.2 \times 10$$^{-9}$$\ \mathrm{C/m}. $$What is the magnitude of the $$y-$$component of the electric field at the position $$(x, y) = (0, 2\ \mathrm{cm})$$?

$$3.2 \times 10^2$\ \mathrm{N/C}$$

Q: A parallel-plate capacitor has plates with area $$0.01\ \mathrm{m}^2$$ and separation $$1\ \mathrm{mm}. If $$the plates are charged to $$5.1\ \mathrm{V}$$, what is the stored energy in the capacitor?

$$1.1 \times 10$$^{-7}$$\ \mathrm{J}$$

Q: An ideal electric dipole with magnitude $$1.5 \times 10$$^{-7}$$\ \mathrm{C \cdot m} is $$placed in a region where the electric field has magnitude $$3.5 \times 10^4$\ \mathrm{N/C}. $$What is the maximum potential energy of the dipole in this field?

$$2.94 \times 10$$^{-3}$$\ \mathrm{J}$$

Q: A sample of a weak acid has a net charge of $$5\ \mathrm{nC}. $$What can you say about the number of electrons compared to protons in the sample?

The number of protons is $$3.1 \times 10$$^{10}$$ more than electrons

Question 1

A collection of 8 point charges, each with charge $$q = 100\ \mathrm{nC}$$, are arranged on the corners of a cube of side length $$10\ \mathrm{cm}. If $$the electric potential is defined to be zero at infinity, what is the potential at the center of the cube?

Accepted Answer

$$6.6 	imes 10^4$\ \mathrm{Volts}$$

Question 2

A charged line segment with charge density $$\lambda = 34\ \mathrm{nanoCoulombs/m}$$ extends along the positive x-axis from the origin to $$x = 50\ \mathrm{cm}. At $$which of the following points does the electric field point parallel to the z-axis?

Accepted Answer

$$(x, y, z) = (25, 0, 50)\ \mathrm{cm}$$

Question 3

Four point charges, each with charge $$q = 7.0\ \mathrm{nC}$$, are arranged in a square with side length $$20\ \mathrm{cm}. $$What is the electric potential at the center of one of the sides of the square?

Accepted Answer

$$716\ \mathrm{Volts}$$

Question 4

A ring of charge with radius $$5\ \mathrm{cm} is $$centered on the origin and located in the $$xy-$$plane. The ring has total charge of $$4\ \mu\mathrm{C}. An $$ideal dipole with dipole moment $$10^{-7}$$\ \mathrm{C \cdot m}$$ is located along the positive z$-axis at z = 5$$\ \mathrm{cm}$$. What is the preferred alignment of the dipole?

Accepted Answer

Parallel to the $$z-$$axis

Question 5

A point charge of $$5\ \mu\mathrm{C} is at $$the origin. A point charge of $$-1\ \mu\mathrm{C} is $$located at $$x = 5\ \mathrm{m}. $$Assuming the electric potential is defined to be zero at infinity, at what other point(s) on the $$x-$$axis is the electric potential zero?

Accepted Answer

$$x = -1.25\ \mathrm{m}$$

Question 6

Four point charges, each with charge $$q = 50\ \mathrm{nC}$$, are arranged in a square with side length $$10\ \mathrm{cm}. If a $$proton is at the center of the square and is given an initial velocity of $$10^5$$\ \mathrm{m/s}$$ in the $$+\hat{y}$$ direction, what is its velocity when it is very far away from the square? (Neglect energy loss, and use m_p = 1.67$$ 	imes $$10^{-27}$$\ \mathrm{kg}$$, q_p = 1.6$$ 	imes $$10^{-19}$$\ \mathrm{C}$$)

Accepted Answer

$$1.4 	imes 10^5$\ \mathrm{m/s}$$

Question 7

Three point charges, each with charge $$q = 72\ \mathrm{nC}$$, are arranged in an equilateral triangle with side length $$1\ \mathrm{m}. $$What is the magnitude of the electrostatic force on one of the charges from the combined electric field of the other two?

Accepted Answer

$$6.1 	imes 10$$^{-3}$$\ \mathrm{N}$$

Question 8

A parallel-plate capacitor has a plate separation of $$1\ \mathrm{mm}$$ and a potential difference of $$5.1\ \mathrm{V}$$ across the plates. What is the magnitude of the electric field between the plates?

Accepted Answer

$$5.1 	imes 10^3$\ \mathrm{N/C}$$

Question 9

Which of the following is true about a conducting object in electrostatic equilibrium?

Accepted Answer

The electric field within the body of the conductor must be zero

Question 10

Suppose there is a semi-infinite line charge along the positive $$x-$$axis with charge density $$\lambda = 2.2 	imes 10$$^{-9}$$\ \mathrm{C/m}. $$What is the magnitude of the $$y-$$component of the electric field at the position $$(x, y) = (0, 2\ \mathrm{cm})$$?

Accepted Answer

$$3.2 	imes 10^2$\ \mathrm{N/C}$$

Question 11

A parallel-plate capacitor has plates with area $$0.01\ \mathrm{m}^2$$ and separation $$1\ \mathrm{mm}. If $$the plates are charged to $$5.1\ \mathrm{V}$$, what is the stored energy in the capacitor?

Accepted Answer

$$1.1 	imes 10$$^{-7}$$\ \mathrm{J}$$

Question 12

An ideal electric dipole with magnitude $$1.5 	imes 10$$^{-7}$$\ \mathrm{C \cdot m} is $$placed in a region where the electric field has magnitude $$3.5 	imes 10^4$\ \mathrm{N/C}. $$What is the maximum potential energy of the dipole in this field?

Accepted Answer

$$2.94 	imes 10$$^{-3}$$\ \mathrm{J}$$

Question 13

A ring of charge with radius $$5\ \mathrm{cm} is $$centered on the origin and located in the $$xy-$$plane. The ring has total charge of $$4\ \mu\mathrm{C}. An $$ideal dipole with dipole moment $$10^{-7}$$\ \mathrm{C \cdot m}$$ is located along the positive z$-axis at z = 5$$\ \mathrm{cm}$$. What is the direction of the electric field at the dipole's location?

Accepted Answer

Along the $$z-$$axis

Question 14

A sample of a weak acid has a net charge of $$5\ \mathrm{nC}. $$What can you say about the number of electrons compared to protons in the sample?

Accepted Answer

The number of protons is $$3.1 	imes 10$$^{10}$$ more than electrons

Question 15

Consider two parallel infinite planes of charge. One is at $$z = 0$$ with charge density $$5\ \mu\mathrm{C/m}^2$$, and the other is at $$z = 1\ \mathrm{m}$$ with charge density $$-3\ \mu\mathrm{C/m}^2. $$What is the electric field in the region $$0 \u003c z \u003c 1$$?

Accepted Answer

$$E = \frac{\$$sigma_1$$ - \$$sigma_2$$}{2\$$varepsilon_0$$}$$

Question 16

A neutral conducting sphere S is brought near a positively charged conductor (without touching). What is the resulting charge distribution on the surface of S?

Accepted Answer

Negative charge accumulates on the side near the conductor, positive on the far side

Physics 2321: Electric Fields, Potentials, and Charge Distributions – Guided Study Notes

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